The half century after Columbus's voyage sees a frenzy of activity in the new world (part exploration, part conquest, part colonization) as the Spanish scramble and struggle to make the most of their unexpected new opportunities.

By 1506 the entire continental shore of the Caribbean Sea has been explored from Honduras to the mouth of the Orinoco. Known at first as Tierra Firme (a phrase applied to the isthmus of Panama), it is believed to be part of the coast of Asia - until Vespucci's furthest journey south gives him a different impression, which becomes gradually accepted.

During the first decade of the century the only secure Spanish settlement in the new world is Santo Domingo, on the island of Hispaniola, established in 1496 by Diego Columbus, brother of the explorer. An equivalently stable settlement is not achieved in continental America until 1510, when Balboa founds Santa María la Antigua del Darién (the site from which, in 1513, he makes his expedition to the Pacific).

Thereafter the speed of Spanish expansion and consolidation over a vast region is astonishing. By 1515, with the conquest of Cuba and the founding of Havana, the islands of the Caribbean are under Spanish control. They become the launch pad for further adventures.

The Aztec kingdom in Mexico is conquered in 1521, followed by a campaign against the Maya in Yucatan. Central America, from Guatemala to Nicaragua, is brought under Spanish control between 1524 and 1526. In the southern part of the continent the coast of Venezuela (where the rich pearl fisheries are a powerful lure) is the first region to attract Spanish settlers, from 1523. Down the west coast, the Inca kingdom in Peru is overwhelmed in 1533; Ecuador and Colombia are subdued later in the 1530s; and most of Chile is gradually brought under control during the 1540s.

On the east coast of the continent Argentina, around the river Plate, is colonized from the 1540s. Brazil, meanwhile, is developing in Portuguese hands.

This half-century of activity by a single nation, Spain, on the other side of a vast ocean, in an age of relatively primitive sailing vessels, is perhaps unparalleled in history. It involves numerous incidents and adventures which demonstrate the courage, greed, cruelty and wanton destructiveness of the Spanish conquistadors ('conquerors').

Two adventures in particular catch the imagination of their own time and of every age since. They are the victories won against the greatest odds and for the richest gains - the toppling by a handful of Spaniards of the great empires of the Aztecs and the Incas. But the first important development in contintental America is the establishment of Panama.

Panama: from1519

After Balboa discovers the Pacific in 1513, he is given responsibility for Spain's new ocean. But the bitter rivalry of Pedrarias, governor of the neighbouring crown colony, prevents Balboa from making anything of his new appointment.

Instead it is Pedrarias who establishes a new Spanish municipality and bishopric on the south coast of the isthmus at Panama, in the year 1519 - within month's of his judicial murder of his rival.

Panama immediately becomes a place of focal importance in the developing Spanish empire. From here expeditions set out to colonize the Pacific coast (most notable being the departure of Pizarro on his voyage to Peru in 1530). And here the produce of the Pacific colonies is subsequently brought, to start its journey to Spain.

The goods are carried on caravans of mules for fifty miles across the isthmus to Portobelo - a harbour named beautiful by Columbus in 1502. Portobelo becomes the scene of a great trade fair. Each year, until the event is discontinued in 1748, a fleet of Spanish galleons arrives, to deliver European goods for the colonies and to take home the wealth of Latin America.

A glimpse of Aztec gold: 1518

In the summer of 1518 a meeting takes place, on the Caribbean coast of Mexico, between a party of Spanish explorers and the retinue of a local chieftain. The two sides can communicate only in signs, but an exchange of presents confirms the amicable mood. The Spaniards hand over glass beads, iron pins and scissors. They are astonished to receive in return superbly worked golden ornaments and vessels.

The Indian chieftain sends news of these bearded strangers to his lord, the Aztec emperor. Their arrival suggests to the Aztecs that the exiled Quetzalcoatl may be about to return. This god-king should, for safety's sake, be appropriately welcomed.

The golden objects are dutifully sent back by the Spanish commander to his superiors in Cuba. From there, with equal decorum, the king's share of the treasure is despatched to Spain. The effect of this gold is immediate. An expedition is rapidly prepared to invade the wealthy kingdom now known to exist in Mexico.

The choice of leader falls upon Hernando Cortes. A lawyer and farmer, he has been in the new world since 1504 and has become an established figure, first in Hispaniola and then in Cuba. But this is his first important command.

Cortes advances into Mexico: 1519

Cortes reaches the coast of Mexico, in March 1519, with eleven ships. They carry some 600 men, 16 horses and about 20 guns of various sizes. The Spanish party is soon confronted by a large number of Indians in a battle where the effect of horses and guns (both new to the Indians) is rapidly decisive. Peace is made and presents exchanged - including twenty Indian women for the Spaniards. One of them, known to the Spaniards as Doña Marina, becomes Cortes' mistress and interpreter.

Cortes then sails further along the coast and founds a settlement at Veracruz, leaving some of his party to defend it.

Before proceeding inland, Cortes makes a bold gesture. He sinks ten of his ships, claiming that they are worm-eaten and dangerous. The single surviving vessel is offered to any of his soldiers (and now sailors too, about 100 in all, liberated from their previous duties) who would prefer to return immediately to Cuba, publicly admitting that they have no stomach for the great task ahead. No one takes him up.

His small party is now irretrievably committed to the success of the adventure. Cortes leads them into the interior of the country.

The next battles, far more dangerous than the first encounters on the coast, are with the Tlaxcala people. The Spaniards eventually defeat them, and are received as conquerors in their capital city. This is a victory of great significance in the unfolding story, for the Tlaxcaltecs are in a state of permanent warfare with their dangerous neighbours. Any enemy of the Aztecs is a friend of theirs. They become, and remain, loyal allies of the Spaniards in Mexico.

In November 1519 when Cortes approaches Tenochtitlan, the capital of the Aztecs, his small force is augmented by 1000 Tlaxtalecs. But to the astonishment of the Spaniards, no force is needed.

Cortes and Montezuma: 1519-1520

The Aztec emperor, Montezuma II, has had plenty of warning of the arrival of the fair-skinned bearded strangers. He also knows that this is a One-Reed year in the Mexican calendar cycle, when the fair-skinned bearded Quetzalcoatl will at some time return.

He sends the approaching Spaniards a succession of embassies, offering rich gifts if they will turn back. When these fail, he decides against opposing the intruders with force. Instead Cortes is greeted in Tenochtitlan, on 8 November 1519, with the courtesy due to Quetzalcoatl or his emissary. In the words of one of the small band of conquistadors, they seemed to have Luck on their side.

For a week Cortes and his companions enjoy the hospitality of the emperor. They sit in his hall of audience and attempt to convert him to Christianity. They clatter round his city on their horses, in full armour, to see the sights (they are particularly shocked by the slab for human sacrifice and the newly extracted hearts at the top of the temple pyramid).

But Cortes is well aware of the extreme danger of the situation. He devises a plan by which the emperor will be removed from his own palace and transferred to the building where the Spaniards are lodged.

The capture of the emperor is carried out with a brilliantly controlled blend of persuasion and threat. The result is that Montezuma appears to maintain his full court procedure under Spanish protection. A few hundred Spaniards have taken control of the mighty Aztec empire.

During the next year, 1520, chaos and upheaval result from the approach of a rival Spanish expedition, launched from Cuba to deprive Cortes of his spoils. He is able to defeat it, but at a high price. In his absence the 80 Spaniards left in Tenochtitlan lose control of the city - largely thanks to their own barbarous treatment of the inhabitants.

When Cortes returns, he finds garrison and emperor besieged together. He persuades Montezuma to address his people from a turret, urging peace. The hail of missiles greeting this attempt leaves the emperor mortally wounded.

The situation is now so desperate that Cortes withdraws his army from the city in haste, in July 1520, during 'the Sorrowful Night'. With Tlaxcala assistance he captures it again a year later, on 13 August 1521. There is no further Aztec resistance. The conquest of central Mexico is complete.